TY - JOUR
T1 - Spectra of regular graphs and hypergraphs and orthogonal polynomials
AU - Li, Wen Ch ing Winnie
AU - Solé, Patrick
N1 - Funding Information:
We thank the anonymous referee for helpful remarks. The Research of the first author was supported in part by NSA grants MDA904-92-H-3054 and MDA904-95-H-1006. The research of the second author was supported in part by a joint CNRS-NSF grant. The second author is on leave of absence from CNRS-I3S, France, and would like to thank the Mathematics Department of Pennsylvania State University for its hospitality.
PY - 1996/7
Y1 - 1996/7
N2 - In this paper we study the distribution of eigenvalues of regular graphs, regular hypergraphs, and biregular bipartite graphs of given girth by considering the polynomials orthogonal with respect to the measures attached to the spectra of such graphs and to the continuous spectra of their 'universal covers'. Our estimates are tight for Biggs graphs and generalized polygons. We also give an application to the distribution of eigenvalues of Hecke operators acting on weight 2 cusp forms for certain congruence subgroups.
AB - In this paper we study the distribution of eigenvalues of regular graphs, regular hypergraphs, and biregular bipartite graphs of given girth by considering the polynomials orthogonal with respect to the measures attached to the spectra of such graphs and to the continuous spectra of their 'universal covers'. Our estimates are tight for Biggs graphs and generalized polygons. We also give an application to the distribution of eigenvalues of Hecke operators acting on weight 2 cusp forms for certain congruence subgroups.
UR - http://www.scopus.com/inward/record.url?scp=21344435017&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=21344435017&partnerID=8YFLogxK
U2 - 10.1006/eujc.1996.0040
DO - 10.1006/eujc.1996.0040
M3 - Article
AN - SCOPUS:21344435017
SN - 0195-6698
VL - 17
SP - 461
EP - 477
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 5
ER -